I thought about using Dropbox as a location for a repo. It doesn't take much thought to realize why this isn't safe.
If you push to a shared Dropbox based repo, Dropbox will detect the changes and begin syncing everyone else's copy. If someone else tries to read at that moment, they will get an inconsistent view, and if they try to do a commit or push themselves you are likely to see corruption as Dropbox and Git's writes clobber one another.
Clobbering repos is bad. Don't do that. Use GitHub instead, or a virtual server running something such as Gitolite and GitLab.